1. Introduction
The presence of electromagnetic fields (EMFs) arising from both natural and artificial sources represents a ubiquitous phenomenon in the human environment [
1]. The natural origins of EMFs, such as the Sun, the Earth’s natural electric and magnetic field, cosmic radiations, and atmospheric discharges, were the only sources during the longest period of evolutionary development. The 20th century brought a sudden expansion of artificial (human-made) field sources, which are nowadays mostly due to the wireless transmission technology (WTT) [
2]. Playing a key role in today’s communication, the WTT represents a wireless modality for data transfer by means of electromagnetic waves, and has become of huge practical importance in our daily activities. As such, this modality is central to emerging technologies over the next years, including 5G/6G cellular systems [
3,
4], new medical devices [
5], robots and drones [
6], self-driving vehicles [
7], etc. By increasing the number of EMF sources, the intensity of EMF also increases. This increase can be induced by higher power transmitters (radio and TV transmitters, mobile phone base stations), as well as by the low-power devices that we use every day, such as mobile phones, microwave ovens, Wi-Fi routers, etc. An unavoidable effect of these phenomena is the chronic exposure of the population to EMF values, to an extent such that the exposure on wireless communication networks is often cited as a major cause of public concern about possible adverse effects of EMFs on health [
8]. Accordingly, the scientific studies of EMF intensity treat this aspect as one of the most crucial, including recommendations by national and international health/scientific authorities, such as the International Commission on Non-Ionizing Radiation Protection, ICNIRP [
9], for establishing safety limits for exposure to EMFs.
A relevant aspect in the study of EMFs, besides measuring the average intensity over a certain period, refers to the temporal variability of the electric field (EF) monitored during that period. A relevant question, raised in this work, is how the presence/absence or temporary gathering of people who use wireless communication services affects the variability over time of the EF intensity. To address this question, we perform a thorough analysis of the temporal statistical structure of time series reflecting cumulative intensity of wideband EFs. The time series are acquired by a sensor placed in the campus area of the University of Novi Sad, Serbia, during two consecutive years, 2019 and 2020. Analyzing data from this recording site allows us to investigate the underlying intrinsic dynamics of EF intensity depending on human mobility and gathering. The analysis of human mobility as a dynamic phenomenon has been extensively performed in the last two decades by interdisciplinary studies aimed to understand the intrinsic properties of human movements and the mechanisms behind the detected patterns [
10,
11], and to determine the effects of these patterns on the structure and dynamics of social networks [
12,
13], on economic phenomena [
14], and recently even on the transmission of the COVID-19 disease [
15,
16]. While human mobility is typically analyzed by the direct use of cellular phone data through the global navigation satellite system (GNSS), here we deal with this concept (more precisely, with people absence/presence or gathering in the location of interest) implicitly, by observing its overall effects on the time series of EF intensity. Specifically, the availability of longitudinal data collected continuously over two years in the observed location offers the possibility to explore the effects of human presence and its extent on the dynamic changes of the EF intensity. These changes are related to contributions arising from EF sources linked to human utilization of wireless communication systems and the corresponding services, and thus have the potential to provide additional and complementary information to the one which can be gathered by GNSS data.
The dynamic patterns of EF intensity measured by the considered sensor capture different scenarios of human mobility, including the daily movements of university staff and students within the campus, the decreased mobility during weekends, the less regular gathering of people in the periods of university exams, the considerably reduced presence of university population during holidays and summer break, and—in the analyzed years—the blocked or restricted mobility of the university population due to the state of emergency related to the COVID-19 pandemic. To properly investigate this complex process featuring dynamic patterns deployed across multiple temporal scales, we use both simple statistics (mean, variance) and information-theoretic measures of dynamical complexity implemented through a multiscale approach. Specifically, we characterize the EF intensity time series using the information storage (
), a measure quantifying the amount of uncertainty about the present state of a dynamic system that can be resolved by the knowledge of its past states [
17]. Recognized as one of the three key components of information processing (i.e., information storage, transfer, and modification) [
18],
reflects the regularity of the dynamic patterns in a time series, and has been applied with broad relevance in diverse real-world dynamical systems ranging from human–brain networks [
19] and robot motion [
20] to cardiorespiratory [
21] and cardiovascular [
22] dynamics. The popularity of dynamical information measures like
stems primarily from their generality and applicability to short-length and noisy processes, which allow for characterizing the dynamical nature of the systems generating the observed time series in an efficient and robust way. Besides studying the temporal variability of the EF intensity and its regularity, in this work, we combine the estimation of
[
23] with the method of surrogate data [
24], to investigate the presence of nonlinear dynamics in such time series. In addition, to account for the possible coexistence of oscillatory behaviors at different temporal scales, we follow a multi-scale approach [
25], whereby
is computed after “rescaling” the observed process to focus on a specific range of temporal scales; rescaling is performed by filtering out the fast temporal features from the observed EF time series before the computation of
. The resulting time series, mapping the average EF intensity collected at time scales of 6 min, 30 min, 2 h, and one day, and analyzed respectively over epochs lasting one day, one week, one month, and one year, are investigated to capture the multiscale complexity and nonlinearity of the dynamic changes of EF exposure before and during the COVID-19 pandemic.
3. Results and Discussion
Figure 1 shows a representative time series of the EF intensity observed during a representative day (a), week (b), and month (c) of 2019 and 2020, as well as during the whole year (d). We selected the 79th day, the 15th week, and the fourth month of 2019 and 2020, to compare the EF intensities before and during the COVID-19 pandemic; the series shown in
Figure 1a–c is rescaled according to the coarse-graining procedure described in
Section 2.2, to demonstrate the oscillations dominant in daily, weekly, and monthly observation windows.
Differences between the behavior of the EF intensity during the same period of the two years can be noticed immediately through simple visual inspection. The time series measured in 2019 (orange curves) clearly demonstrate a modulation of the EF intensity which follows the day-to-night cycle (
Figure 1a,b, left) and a reduction in amplitude during the weekends (
Figure 1c, left); we ascribe such modulations to the higher or lower amount of people present in the University area. When the same periods of 2020 are considered (green curves), the day-to-night variations are damped (
Figure 1a,b, right) and do not differ anymore between weekdays and weekends (
Figure 1c, right). We note that the difference between the EF intensities of the same periods of the two years appears evident by looking at the amplitude of the oscillations, but not at the mean values which are roughly the same. Moreover, these differences are not straightforward when the whole-year time series are observed (orange curve vs. green curve in
Figure 1d).
To make the observations above quantitative and confirm them in a complete analysis, we report in
Figure 2 and
Figure 3 the mean
and the variance
of the EF intensity observed at the four time scales and computed for each observation window during the two years. While the mean values of the EF intensity measured in 2019 and 2020 are quite similar (
Figure 2d:
= 1.16 V/m in 2019 and 1.26 V/m in 2020), the dynamic behavior of the mean EF intensity emerges, analyzing the rescaled time series (
Figure 2a–c), which display values oscillating between ∼0.2 V/m and ∼1.9 V/m. The trends of the mean EF intensity show oscillatory activity with a period of one week at the finer time scale (
Figure 2a), as well as slower variations demonstrated when the time scale becomes more coarse (
Figure 2b,c). Given that the oscillations with one-week period observed in the two years (green and orange curves in
Figure 2a) exhibit minimum EF intensity during weekends, they can be related to the amount of people present on the university campus. However, when we compare 2019 and 2020, the averaged EF intensity is different between periods of the two years, which are expected to be similar in terms of human presence (e.g., the first three months where
is higher in 2019, the last three months where
is higher in 2020, and the periods of exams in person and summer pause where
is again higher in 2020). This effect is clearly evident observing also the slower trends in
Figure 2b,c, thus reflecting the contributions from all detected EF sources in the proximity of an installed sensor. Nevertheless, an effect of the pandemic on the mean EF values occurs in correspondence with the State of Emergency (SoE) declared by the Government of Serbia on 15 March 2020 [
41]: starting from this date, wherein strict movement restrictions were implemented, a sudden drop of
is visible at the daily and weekly observation windows (
Figure 2a,b), and the reduced mean field value of ∼1.3 V/m is maintained during the spring and summer 2020, when a clear reduction in the amplitude of oscillations with one-week period is also observed (light orange, green and grey areas in
Figure 2a).
The most distinctive feature that differentiates the mean EF intensity measured during the pandemic and in the preceding year without mobility restrictions is the dampening of the oscillations with a period of one week (
Figure 2a, color-shaded areas). This behavior, suggesting that reduced mobility decreases the variability of the EF intensity more than its mean, becomes straightforward when the variance of the EF time series is analyzed (
Figure 3). In fact, the analysis of EF variability documents very clearly that the variance
drops dramatically (from 0.2–0.3 V
/m
to almost zero) when the SoE is declared, and remains at very low values for the whole period of mobility restrictions when University teaching shifted to the online modality (
Figure 3a,b). The two periods of University exams are characterized by very comparable values of
in 2019 and 2020, which is in line with the fact that, in Serbia, the exams were held in person even during the pandemic. During the summer pause in August, the variance of the EF intensity was comparably very small in 2019 and 2020, while differences arise again during the fall when teaching was ordinarily in person in 2019 and again in online modality in 2020. These patterns of variability of the EF intensity are well-characterized at all time scales, as they are visible over observation windows of one day (
Figure 3a), one week (
Figure 3b), and one month (
Figure 3c). The overall result is that the variability estimated on a yearly basis is lower in 2020 compared to 2019 (
Figure 3d).
The results presented above indicate that the restrictions to mobility imposed by the COVID-19 pandemic (SoE, 2020) or the substantial absence of University population during the summer break (during both 2019 and 2020) affected primarily the variability of the electric fields measured by the sensor of the EMF RATEL system, and only to a lower extent the average field intensity. Here, it is worth noting that the monitoring sensor is installed on the roof of the Faculty of Technical Sciences (FTS), placed in the campus area of University of Novi Sad (the images following the sensor position can be found in the link [
42]). Besides the FTS, the campus area encompasses six faculties more, while the FTS presents the largest one by the number of students. However, since the substantial reduction in the presence of people during the pandemic and summer break in such highly-populated area during the regular university life (teaching and exam periods) affected dominantly the variability of EF intensity series, to investigate the changes that originate this variability and its modification in different conditions, we move to study the storage of predictable information within the EF intensity time series observed at different time scales.
Figure 4 depicts the results the analysis of information storage performed for the representative time series reported in
Figure 1, pre-processed as explained in
Section 2.2. All the estimates of
resulted n being statistically significant according to the test based on randomly shuffled surrogate data, meaning that the null hypothesis of a serially uncorrelated process was rejected for all the series in
Figure 1 (data not shown). The amount of information stored in the EF dynamics is always higher for the exemplary time series measured during 2019 than for the series measured in the same period of 2020, with values
= 0.42 nats and
= 0.2 nats for the 79th day (
Figure 4a),
= 1.45 nats and
= 0.62 nats for the 15th week (
Figure 4b),
= 1.33 nats and
= 0.89 nats for the 4th month (
Figure 4c), and
= 0.65 nats and
= 0.44 nats for the whole year (
Figure 4d). The lower values of IS reflect higher complexity of the EF time series, documenting the presence of less predictable, more erratic EF dynamical patterns when human mobility was strictly restricted, i.e., during 2020 due to COVID-19 pandemic, in contrast to one year before when the higher IS values indicate the presence of more regular patterns of EF intensity. Nonetheless, the analysis based on IAAFT surrogate data reveals for all time scales the presence of nonlinear EF dynamics during 2019 (the original
value exceeds the
surrogate threshold in
Figure 4a–d), while, on the contrary, the daily, weekly, and monthly dynamics observed during the same periods in 2020 can be regarded as linear (the original
value is below the surrogate threshold in
Figure 4a–c). This result distinguishes the nature of oscillations during the periods of normal and restricted mobility, also showing how complexity and nonlinearity are different concepts: in this case, the less complex dynamics (showing higher
) are those with a stronger contribution of nonlinearities (
is higher than the nonlinearity threshold).
The complete multiscale analysis was performed to investigate the trends of the information stored in the time series of EF intensity analyzed separately during 2019 and 2020 over daily, weekly, and monthly observation windows as well as over the whole year. According to the surrogate data analysis based on random shuffling, the null hypothesis of white noise process was rejected for all cases, thus assessing statistically the significance of the values in all the analyzed time series (data not shown). The detection of statistically significant multiscale information storage is in line with the existence of predictable dynamics in the series measured at different scales, indicating that the EF intensity is a complex but structured process characterized by regular oscillations across multiple scales of observation, which reflect an alternating presence of EF sources presumably related to human utilization of wireless communication services.
The values of information storage measured over observation windows of different length, each characterized by their peculiar time scale, are reported in
Figure 5. The detailed analysis comparing the two considered years of EF recordings sheds further light on the nature of these predictable patterns. In fact, as a consequence of the onset of the COVID-19 pandemic in March 2020 and of the establishment of strict mobility restrictions, the EF intensity time series displays a significant reduction in the values of
. The reduced regularity compared with the same period of the preceding year is visible in the EF dynamics observed on a daily basis (
Figure 5a, light orange areas) as well as when investigating longer time-scales which cover observation windows of one week (
Figure 5b, light orange areas) or of one month (
Figure 5c, months 3, 4, 5). The presence of more erratic multiscale patterns of EF intensity is associated with the significantly reduced access of people to the university campus in this period when teaching lessons were delivered in the online modality.
At the highest level of coarse graining, the difference between dynamic behavior of the EF intensity measured during the two years is documented by the lower regularity measured during 2020 than in 2019 (
Figure 5d:
= 0.65 nats and
= 0.44 nats). On the other hand, the information stored in the EF intensity time series takes comparable values in the two years during the periods of university exams and summer pause (light green and grey areas in
Figure 5a,b and months 6–9 in
Figure 5c). In this time frame, the
values are relatively high during the exam periods and decrease to lower values during the summer, suggesting that the predictability of the field intensity dynamics arises from regular movement of people within the area covered by the EF sensor. The similarity between the two years can be explained considering that the campus was populated in a similar way as exams were always delivered in person during the pandemic. Then, the prosecution of the online teaching modality during the fall/winter semester of 2020 determined lower and less regular EF dynamics compared to the fall/winter of 2019; again, the phenomenon is visible at all time scales (light yellow area in
Figure 5a,b and months 10–12 in
Figure 5c).
As regards the nature of the oscillatory patterns underlying the observed dynamics, the use of IAAFT surrogate time series led us to detect the coexistence of linear and nonlinear dynamics in the day-by-day EF activity monitored at the finer time scale; this result is depicted in
Figure 5a where the daily dynamics detected as linear are marked with a black square. When the dynamics are observed on a coarser time scale, we notice that many of the lower
values measured during periods of restricted mobility in 2020 are associated with linear dynamics, while the corresponding periods in 2019 showing higher
values also display nonlinear dynamics. This happens for instance comparing the weeks and months covering the population lockdown in spring 2020 with the same periods in 2019 (
Figure 5b,c); the effect is documented clearly for the time series of the 4th month shown in
Figure 1c and characterized by the
patterns of
Figure 4c: the highly predictable and nonlinear EF dynamics observed in April 2019, resulting from the occurrence of day-night oscillations modulated in amplitude by a slower rhythm with one-week period, are destroyed in April 2020, where the regularity as well as the richness of the dynamics are lost. These findings suggest that both predictability and nonlinearity of the EF intensity time series are lost as a consequence of the restrictions to mobility caused by the COVID-19 pandemic during April and May 2020. A similar effect is observed in August of both years when, due to the summer pause, the campus area is characterized by a lower and less regular presence of university staff and students. Therefore, we conclude that periods characterized as less populated determine not only a decrease of the EF variability, but also an increase of the complexity of the EF patterns and a simultaneous loss of nonlinear dynamics in these patterns.
4. Conclusions and Future Perspectives
The results of this study indicate that the EF intensity measured in an urban area with significant movements of people gives rise to time series which can be described as the output of a dynamical system endowed with complex nonlinear and multiscale dynamics. Moreover, the dynamic behavior of the EF intensity can change its properties depending on the temporary accumulation, in proximity of the recording sensor, of EMF sources which can be associated with human utilization of wireless communication systems. Those sources likely refer to mobile telephony systems, including both mobile phones and their base stations installed in the campus area [
43], which produce radio-frequency radiation as a means of their communication; these systems integrate phone calls with several features like the Bluetooth and Wi-Fi, which are used by the university population also through other devices like tablets, laptops, and desktop computers. Another example refers to modern vehicles which receive relevant traffic information by using wireless communications from their peers. We find that, in the periods of significantly reduced circulation of university staff and students (e.g., due to summer breaks or to the restrictions to mobility related to the COVID-19 pandemic), not only the amplitude of the oscillations of EF intensity observed at different time scales varied significantly, but also the EF patterns became simultaneously more complex and more linear. These findings document on the one hand the importance of employing non-parametric model-free approaches to fully capture the dynamics of complex systems like this [
23], and on the other hand confirm the evidence proven for other types of dynamic systems (e.g., the human heart rate [
40]) that complexity and nonlinearity are different, often complementary concepts.
It is worth stressing that the time series of EF variability analyzed here, probing the cumulative intensity of EFs emitted by sources located in the vicinity of the recording sensor, can to some extent be regarded as measurements of human mobility patterns. Hence, our statistical analysis can describe, at the integrated level, the impact of pandemics on human mobility on the territory under study. Different forms of lockdown worldwide, introduced by the Governments to flatten the curve of new infections, affected human mobility both globally and locally on unprecedented scales; the study of implications found in this research can also serve as an opportunity to propose strategies for monitoring and stimulate a more sustainable human mobility. Many recent studies focused on micro-mobility data and analyze the changes in micro-mobility usage before and during the lockdown period exploiting high-resolution micro-mobility trip data [
44,
45]. From this perspective, our study supports the idea that EF intensity measurements may be complementary to data collections like those from mobile phones, and might be employed to investigate changes in the patterns of mobility both during pandemics or other kinds of events.
A limitation in the exploitation of the data analyzed in this work for the analysis of human mobility may come from the fact these data are recorded in the form of cumulative EF measurements, covering a broad range of frequencies, thus being influenced by EMF sources other than those related to people’s presence and their usage of communication services. This aspect, as well as the possibility of installation of new EMF sources in the campus area, which are likely the main reasons for the presence of mean EF patterns with difficult interpretation observed in some periods of the two analyzed years (
Figure 2), have been mitigated in the present study by focusing on measures of variance rather than mean and by performing multiscale analysis of regularity (
Figure 3,
Figure 4 and
Figure 5). Nevertheless, the utilization of frequency-selective measurements may, improve the capability of measures like those proposed in this work to capture a more tight link between human movements and the dynamical patterns of EF intensity.
The interpretation of EF data as time series measuring the temporal variability of the EF intensity can have practical implications also on the assessment of safety related to the spread of EMF sources, and on the plans for expanding the network of sensors in a sustainable and strategic direction. In fact, our approach can be exploited as a supportive tool for the further modeling of network architecture towards more scalable, secure, and cost-effective solutions, which are the requirements of the smart city concept intended as a form of intelligent and sustainable urban development [
46]. In this context, future work is envisaged to move towards the study of the joint information shared by multiple EF time series [
22], which would open up the possibility of investigating how sensor networks implemented within a territory are functionally interconnected, also providing criteria for the strategic placement/optimization of new sensors both at a local and at a national level.